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arxiv: 2604.02712 · v1 · submitted 2026-04-03 · 💻 cs.GT

Recognition: 2 theorem links

· Lean Theorem

Maximally Random Sortition

Gabriel de Azevedo , Paul G\"olz
Authors on Pith no claims yet

Pith reviewed 2026-05-13 18:59 UTC · model grok-4.3

classification 💻 cs.GT
keywords citizens assembliessortitionmaximum entropysampling algorithmsrandom selectiondiversityrepresentationdemocratic innovation
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0 comments X

The pith

Sampling from maximum-entropy distributions over panels yields higher diversity and better constraint satisfaction in citizens' assemblies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops algorithms that draw random panels by maximizing the entropy of the probability distribution over all possible combinations of members. These algorithms can also enforce limits on how frequently any single person is selected. When tested against dozens of real assembly lotteries, the maximum-entropy samples produce panels with stronger intersectional diversity and a higher chance of meeting representation rules that were not known at selection time. The methods are shown to resist strategic manipulation and to support transparent explanation of why any given panel was chosen. One such algorithm has been released as a practical tool for assembly organizers.

Core claim

We design algorithms that sample from maximum-entropy distributions over possible panels, possibly subject to constraints on individual selection probabilities, and show that the resulting panels achieve favorable intersectional diversity and unseen-constraint satisfaction on real assembly data while remaining resistant to manipulation and transparent.

What carries the argument

Maximum-entropy distribution over the combinatorial set of admissible panels, sampled subject to per-person probability bounds.

If this is right

  • Panels drawn this way show measurably higher intersectional diversity on historical assembly data.
  • They satisfy a larger fraction of representation constraints that were not imposed during sampling.
  • The sampling procedures resist manipulation by any single participant or small coalition.
  • The selection process can be explained to participants without revealing private information.
  • One version of the algorithm is already deployed for use by assembly practitioners.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same entropy-maximization approach could be adapted to other large-scale random-selection tasks such as jury pools or participatory budgeting committees.
  • It offers a concrete way to trade off explicit fairness constraints against implicit diversity without requiring exhaustive enumeration of all panels.
  • Future deployments could test whether different entropy formulations (e.g., conditional on demographic margins) produce stable improvements across multiple elections.
  • Open-source implementations would let organizers rerun selections with new constraints and immediately observe the effect on entropy and diversity metrics.

Load-bearing premise

Maximizing entropy under the chosen constraints produces panels that are meaningfully fairer or more diverse without introducing hidden biases from the entropy objective itself.

What would settle it

A side-by-side run on a real assembly lottery in which a maximum-entropy panel scores lower on measured diversity or satisfies fewer post-hoc representation constraints than a uniform random draw from the same pool.

Figures

Figures reproduced from arXiv: 2604.02712 by Gabriel de Azevedo, Paul G\"olz.

Figure 1
Figure 1. Figure 1: Strip plots for the selection probabilities, each point represents a pool member and its position [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Generalization probabilities. Points are colored according to the probability that a uniform set of [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Planned interface of Panelot for choosing the selection algorithm (left) and visualization of the state [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 9
Figure 9. Figure 9: Generalization probabilities colored by organization. [PITH_FULL_IMAGE:figures/full_fig_p032_9.png] view at source ↗
read the original abstract

Citizens' assemblies are a form of democratic innovation in which a randomly selected panel of constituents deliberates on questions of public interest. We study a novel goal for the selection of panel members: maximizing the entropy of the distribution over possible panels. We design algorithms that sample from maximum-entropy distributions, potentially subject to constraints on the individual selection probabilities. We investigate the properties of these algorithms theoretically, including in terms of their resistance to manipulation and transparency. We benchmark our algorithms on a large set of real assembly lotteries in terms of their intersectional diversity and the probability of satisfying unseen representation constraints, and we obtain favorable results on both measures. We deploy one of our algorithms on a website for citizens' assembly practitioners.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes sampling panels for citizens' assemblies from maximum-entropy distributions, possibly subject to constraints on individual selection probabilities. It develops algorithms for this task, analyzes their theoretical properties including resistance to manipulation and transparency, benchmarks them on a large set of real assembly lotteries for intersectional diversity and probability of satisfying unseen representation constraints (reporting favorable results), and deploys one algorithm on a practitioner website.

Significance. If the central empirical claims hold after isolating the contribution of the entropy objective, the work offers a principled information-theoretic framework for sortition that can improve diversity and fairness in democratic innovations while preserving randomness. The combination of theoretical analysis, real-data benchmarks, and practical deployment strengthens its potential impact in the field of algorithmic fairness for public decision-making.

major comments (2)
  1. [Empirical evaluation] Empirical evaluation (benchmarks section): All reported algorithms operate under explicit constraints on individual selection probabilities, yet the headline claim attributes gains in intersectional diversity and unseen-constraint satisfaction to entropy maximization. An ablation that holds the marginal probabilities fixed and compares only the objective (maximum-entropy versus uniform sampling) is required to establish that the reported improvements are due to the entropy criterion rather than the constraints themselves.
  2. [Theoretical analysis] Theoretical properties (analysis section): The manuscript states that the algorithms are resistant to manipulation and transparent, but the precise statements, assumptions, and proofs for these properties under the constrained maximum-entropy distributions are not clearly delineated; without them it is difficult to assess whether the properties survive the addition of probability constraints.
minor comments (1)
  1. [Notation and definitions] Notation for the maximum-entropy objective and the constraint sets should be introduced once with a single consistent symbol set to avoid ambiguity when moving between the algorithmic descriptions and the benchmark results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address the major comments point by point below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Empirical evaluation] Empirical evaluation (benchmarks section): All reported algorithms operate under explicit constraints on individual selection probabilities, yet the headline claim attributes gains in intersectional diversity and unseen-constraint satisfaction to entropy maximization. An ablation that holds the marginal probabilities fixed and compares only the objective (maximum-entropy versus uniform sampling) is required to establish that the reported improvements are due to the entropy criterion rather than the constraints themselves.

    Authors: We agree that a direct ablation isolating the entropy objective is needed. The current benchmarks compare algorithms that may differ in both their objective and constraint sets; we did not explicitly hold marginal probabilities fixed while contrasting maximum-entropy sampling against uniform sampling. We will add this ablation to the benchmarks section, reporting results on intersectional diversity and unseen-constraint satisfaction under identical marginal constraints. revision: yes

  2. Referee: [Theoretical analysis] Theoretical properties (analysis section): The manuscript states that the algorithms are resistant to manipulation and transparent, but the precise statements, assumptions, and proofs for these properties under the constrained maximum-entropy distributions are not clearly delineated; without them it is difficult to assess whether the properties survive the addition of probability constraints.

    Authors: We appreciate the request for greater precision. The analysis section discusses resistance to manipulation and transparency, but the formal statements and assumptions for the constrained case are not stated as explicitly as they should be. We will revise the section to provide clear formal statements, list all assumptions, and include proof sketches showing that the properties continue to hold when individual selection probabilities are constrained. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard max-entropy to new domain

full rationale

The paper's core contribution is the application of maximum-entropy sampling (a standard information-theoretic objective) to panel selection under marginal probability constraints. Theoretical properties follow directly from convex optimization and entropy definitions without self-referential reduction. Benchmarks compare implemented samplers on real data but do not rely on fitted parameters renamed as predictions or load-bearing self-citations. No equations or claims reduce by construction to inputs; the derivation chain remains independent of the target results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work rests on the standard maximum-entropy principle from information theory and basic probabilistic sampling; no new free parameters, axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5406 in / 998 out tokens · 35220 ms · 2026-05-13T18:59:10.982965+00:00 · methodology

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Reference graph

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